Define as , and . Prove by induction that

Proof:

Let P(n) be the propositional statement for n>1 " "

The LHS of P(2) is 5^2-2^2=21 and the RHS if P(2) is 7(3)-10(0)=21. So P(2) is true.

Now assume that P(j) is true for all j<k. That is assume . Then by this assumption that P(j-1) can be written as

Now I'm kind of stuck. This is either going to take some sick algebra or I made a boo-boo.